Often times it is sufficient to know the rough size of a
number, rather than its exact value. For example, a human can
reason about which store to visit to buy milk if one store is
roughly $1$ kilometer
away, and another store is roughly $100$ kilometers away. The exact
distance to each store is irrelevant to the decision at hand;
only the sizes of the numbers matter.
For this problem, determine the ‘size’ of the factorial of
an integer. By size, we mean the number of digits required to
represent the answer in base-$10$.
Input consists of up to $10\,
000$ integers, one per line. Each is in the range
$[0,1\, 000\, 000]$. Input
ends at end of file.
For each integer $n$,
print the number of digits required to represent $n!$ in base-$10$.
|Sample Input 1
||Sample Output 1